Efficient detection of globally optimal surfaces representing object boundaries in volumetric datasets is important and remains challenging in many medical image analysis applications. This proposal deals with a specific problem of detecting optimal single and multiple interacting surfaces in 3-D and 4-D,including cylindrical shapes, closed-surface shapes, and "complex" shapes. Novel methods allowing incorporation of shape-based a priori knowledge in the optimal surface detection framework will be developed. s The computational feasibility is accomplished by transforming the 3-D graph-searching problem to a problem of computing an optimal closed set in a weighted directed graph. Combining the global optimality with problem-specific objective functions used in the optimization process will facilitate application of the methods to a wide variety of medical image segmentation problems. We hypothesize that image segmentation based on 3-D and 4-D surface detection utilizing optimal graph searching will provide accurate and robust segmentation performance in volumetric image data from a variety of medical imaging sources, offering theoretical efficiency andpractical applicability. We propose to: 1) Develop and validate a method for optimal detection of single and multiple interacting surfaces applicable to biomedical image segmentation in 3-D and 4-D (including cylindrical and closed surfaces). 2) Develop and validate a 3-D and 4-D optimal surface detection method that preserve complex topologies. 3) Develop and validate a 3-D and 4-D optimal surface detection method that incorporates shape priors into the segmentation process. The developed methods will be tested in comparison with state-of-the-art methods utilized today. The methods' performance will be statistically assessed in data samples of sufficient sizes. Public Health relevance: Volumetric image scanners (e.g., computed tomography, magnetic resonance, ultrasound) are increasingly available in medicine, yet the analysis of spatial data is typically performed visually on a slice-by-slice basis. The large amount of volumetric information therefore cannot be fully utilized by the physicians. Image analysis methods such as proposed here allow evaluating the image data objectively in a quantitative manner, promising to substantially impact image-based clinical care.